Directional emphasis in ambisonics

Abstract

Techniques of rendering high-order ambisonics (HOAs) involve adjusting the weights of a spherical harmonic (SH) expansion of a sound field based on weights of a SH expansion of a direction emphasis function that multiplies a monopole density that, when its product with a Green's function is integrated over the unit sphere, produces the sound field. An advantage of the improved techniques lies in the ability to better reproduce directionality of a given sound field in a computationally manner, whether the sound field is a temporal function or a time-frequency function.

What is claimed is: 
     
       1. A method, comprising:
 receiving, by controlling circuitry of a sound rendering computer configured to render directional sound fields for a listener, sound data resulting from a sound field detected at a microphone, the sound field being represented as a first expansion in spherical harmonic (SH) functions and including a vector of coefficients of the first expansion; 
 obtaining, by the controlling circuitry, a vector of coefficients of a second expansion of a direction emphasis field in SH functions, the direction emphasis field producing a direction-emphasized monopole density field upon multiplication with a monopole density field; and 
 performing, by the controlling circuitry, a direction emphasis operation on the vector of coefficients of the first expansion based on the vector of coefficients of the second expansion to produce a vector of coefficients of a third expansion into SH functions, the third expansion representing a direction-emphasized sound field that reproduces a directional sound field with a perceived directionality and timbre. 
 
     
     
       2. The method of  claim 1 , wherein performing the direction emphasis operation includes:
 generating conversion matrix data representing a conversion matrix resulting from conversion of an expansion in pairs of SHs into an expansion over single SHs; and 
 producing the vector of coefficients of the third expansion based on the conversion matrix. 
 
     
     
       3. The method of  claim 2 , wherein generating the conversion matrix data includes:
 generating, as an element of the conversion matrix, a Clebsch-Gordan coefficient representing a weight of a SH function in the expansion in pairs of SHs. 
 
     
     
       4. The method of  claim 2 , wherein performing the direction emphasis operation further includes:
 generating a Kronecker product of the vector of coefficients of the first expansion and the vector of coefficients of the second expansion to produce a vector of coefficient products; and 
 producing, as the vector of coefficients of the third expansion, a product of a transpose of the conversion matrix and the vector of coefficient products. 
 
     
     
       5. The method of  claim 1 , wherein the direction emphasis field is proportional to an ensemble average over time of a power of a magnitude of the monopole density field. 
     
     
       6. The method of  claim 5 , wherein the power is equal to 2, and
 wherein obtaining the vector of coefficients of the second expansion includes:
 generating an ensemble average over time of a Kronecker product of the vector of coefficients of the first expansion and a complex conjugate of the vector of coefficients of the first expansion to produce a first vector of ensemble-averaged coefficient products; 
 generating a Hadamard product of a vector of powers of an imaginary unit and the first vector of ensemble-averaged coefficient products to produce a second vector of ensemble-averaged coefficient products; and 
 producing, as an element of the vector of coefficients of the second expansion, a product of a transpose of the conversion matrix and a corresponding element of the second vector of ensemble-averaged coefficient products. 
 
 
     
     
       7. The method of  claim 1 , wherein the vector of coefficients of the second expansion is based on the vector of coefficients of the first expansion. 
     
     
       8. A computer program product comprising a non-transitory storage medium, the computer program product including code that, when executed by processing circuitry of a sound rendering computer configured to render directional sound fields for a listener, causes the processing circuitry to:
 receive sound data resulting from a sound field detected at a microphone, the sound field being represented as a first expansion in spherical harmonic (SH) functions and including a vector of coefficients of the first expansion; 
 obtain a vector of coefficients of a second expansion of a direction emphasis field in SH functions, the direction emphasis field producing a direction-emphasized monopole density field upon multiplication with a monopole density field; and 
 perform a direction emphasis operation on the vector of coefficients of the first expansion based on the vector of coefficients of the second expansion to produce a vector of coefficients of a third expansion into SH functions, the third expansion representing a direction-emphasized sound field that reproduces a directional sound field with a perceived directionality and timbre. 
 
     
     
       9. The computer program product of  claim 8 , wherein performing the direction emphasis operation includes:
 generating conversion matrix data representing a conversion matrix resulting from conversion of an expansion in pairs of SHs into an expansion over single SHs; and 
 producing the vector of coefficients of the third expansion based on the conversion matrix. 
 
     
     
       10. The computer program product of  claim 9 , wherein generating the conversion matrix data includes:
 generating a plurality of points on a unit sphere; and 
 producing the conversion matrix based on the plurality of points on the unit sphere. 
 
     
     
       11. The computer program product of  claim 9 , wherein performing the direction emphasis operation further includes:
 generating a Kronecker product of the vector of coefficients of the second expansion and a first vector of ones to produce a first product vector; 
 generating a product of a second vector of ones and a transpose of the first product vector to produce a second product vector; 
 generating a Hadamard product of a transpose of the conversion matrix and the second product vector to produce a second conversion matrix; 
 generating a Kronecker product of an identity matrix and a third vector of ones to produce a matrix of units; and 
 producing, as the vector of coefficients of the third expansion, a product of a transpose of the second conversion matrix, the matrix of units, and the vector of coefficients of the first expansion. 
 
     
     
       12. The computer program product of  claim 8 , wherein the direction emphasis field is proportional to an ensemble average over time of a power of a magnitude of the monopole density field. 
     
     
       13. The computer program product of  claim 12 , wherein the power is equal to 2, and
 wherein obtaining the vector of coefficients of the second expansion includes:
 generating an ensemble average over time of a Kronecker product of the vector of coefficients of the first expansion and a complex conjugate of the vector of coefficients of the first expansion to produce a first vector of ensemble-averaged coefficient products; 
 generating a Hadamard product of a vector of powers of an imaginary unit and the first vector of ensemble-averaged coefficient products to produce a second vector of ensemble-averaged coefficient products; and 
 producing, as an element of the vector of coefficients of the second expansion, a product of a transpose of the conversion matrix and a corresponding element of the second vector of ensemble-averaged coefficient products. 
 
 
     
     
       14. The computer program product of  claim 8 , wherein the vector of coefficients of the second expansion is based on the vector of coefficients of the first expansion. 
     
     
       15. An electronic apparatus configured to render directional sound fields for a listener, the electronic apparatus comprising:
 memory; and 
 controlling circuitry coupled to the memory, the controlling circuitry being configured to:
 receive sound data resulting from a sound field detected at a microphone, the sound field being represented as a first expansion in spherical harmonic (SH) functions and including a vector of coefficients of the first expansion; 
 obtain a vector of coefficients of a second expansion of a direction emphasis field in SH functions, the direction emphasis field producing a direction-emphasized monopole density field upon multiplication with a monopole density field; and 
 perform a direction emphasis operation on the vector of coefficients of the first expansion based on the vector of coefficients of the second expansion to produce a vector of coefficients of a third expansion into SH functions, the third expansion representing a direction-emphasized sound field that reproduces a directional sound field with a perceived directionality and timbre. 
 
 
     
     
       16. The electronic apparatus of  claim 15 , wherein the controlling circuitry configured to perform the direction emphasis operation is further configured to:
 generate conversion matrix data representing a conversion matrix resulting from conversion of an expansion in pairs of SHs into an expansion over single SHs; and 
 produce the vector of coefficients of the third expansion based on the conversion matrix. 
 
     
     
       17. The electronic apparatus of  claim 16 , wherein the controlling circuitry configured to generate the conversion matrix data is further configured to:
 generate a plurality of points on a unit sphere; and 
 produce the conversion matrix based on the plurality of points on the unit sphere. 
 
     
     
       18. The electronic apparatus of  claim 16 , wherein the controlling circuitry configured to perform the direction emphasis operation further is further configured to:
 generate a Kronecker product of the vector of coefficients of the second expansion and a first vector of ones to produce a first product vector; 
 generate a product of a second vector of ones and a transpose of the first product vector to produce a second product vector; 
 generate a Hadamard product of a transpose of the conversion matrix and the second product vector to produce a second conversion matrix; 
 generate a Kronecker product of an identity matrix and a third vector of ones to produce a matrix of units; and 
 produce, as the vector of coefficients of the third expansion, a product of a transpose of the second conversion matrix, the matrix of units, and the vector of coefficients of the first expansion. 
 
     
     
       19. The electronic apparatus of  claim 15 , wherein the direction emphasis field is proportional to an ensemble average over time of a power of a magnitude of the monopole density field. 
     
     
       20. The electronic apparatus of  claim 19 , wherein the power is equal to 2, and
 wherein the controlling circuitry configured to obtain the vector of coefficients of the second expansion is further configured to:
 generate an ensemble average over time of a Kronecker product of the vector of coefficients of the first expansion and a complex conjugate of the vector of coefficients of the first expansion to produce a first vector of ensemble-averaged coefficient products; 
 generate a Hadamard product of a vector of powers of an imaginary unit and the first vector of ensemble-averaged coefficient products to produce a second vector of ensemble-averaged coefficient products; and 
 produce, as an element of the vector of coefficients of the second expansion, a product of a transpose of the conversion matrix and a corresponding element of the second vector of ensemble-averaged coefficient products.